Majorchuck,
First off, welcome to the blog and back to the world of shooting and reloading, which provides good clean entertainment for most of us. Sorry to read about the history of why the break in fun. And let me state from the onset, I claim no great expertise, but have shot and continue to shoot a .308 for target accuracy which is now my thing, given I've had enough of the hunting years and my knees aren't what they used to be. Anyways, I agree with what the other have suggested. But, as a thought, .308 has always been an excellent caliber for accuracy and target shooting. But you might conisdeer doing some reading on 6.5mm's and even the .260 that some guys love and swear by. Personally I crave accuracy with each and every load I put together and am in search of that 5 shot one holer regardless of the caliber. But I have seen, first hand the incredible accuracy of the 6mm's, 6.5's even moreso and also the 260's that are extreme impressive at 300+ yds. There is nothing wrong with the .308 and they shoot very well even at 1000 yds, but do not put together as tight a group as the 6's do. SO I thought I'd make mention of some of my thoughts as I have a 6.5 in the works. And I would strongly suggest you stick with a Remington 700 action as the platform for mounting a Match Grade barrel to aid in your efforts in accuracy for Target shooting. There are several manufacturers of Match Grade barrels around including, Shilen, Hart, Broughton, etc and those barrel usually go for between $300 - $325 after looking around or getting one directly from the manufacturer. Now I will admit I am unfamiliar with the current regulations and laws of Canada so some avenues may be closed to you in putting together a rig of your choice.
In any case, good luck in your efforts and may I wish you well. I am always pleased to aid a Canadian friend north of our borders, especially after having had the priviledge of serving more than three years in a small US Army Detachment, stationed in a Nato sector of Germany alongside three forts of the Royal Canadian Regiment & Mechanized Infantry, whose members always took good care of us back in the 60's and early 70's. Hollar if I can be of assistance to you out here in California.